Parabolic Boundary Value Problems in a Piecewise Homogeneous Wedge-Shaped Cylindrical-Circular Layer with a Cavity

The unique exact analytical solutions of parabolic boundary value prob-lems mathematical physics in piecewise homogeneous by the radial variable zwedge-shaped angular cylindrical-circular layer with a cavity were constructed at first time method classical integral and hybrid in-tegral transforms combination main (matrices influence Green matrices) proposed article.The cases assigning on verge wedge conditions 1st kind (Dirichlet) 2nd (Neumann) their possible com-binations (Dirichlet—Neumann, Neumann—Dirichlet) are considered.Finite Fourier transform an variable, finite inte-gral Cartesian segment applicative Weber type polar axis npoints conjugation used to construct investigated problems.The consistent application geometric variables al-lows us reduce three-dimensional initial boundary-value problems Cauchy problem for regular linear inhomogeneous or-der differential equation whose solution iswritten closed form.The inverse ob-tained space images restores consid-ered through image explicit formin originals.At same time, obtained form.